基于狄利克雷过程高斯混合模型的变分推断

Variational inference for Gaussian mixture model based on Dirichlet process

高斯混合模型(Gaussian Mixture Model,GMM)无法通过观测数据来自动选择适当数量的混合物分量,故无法准确描述数据。因此,将狄利克雷过程先验与GMM相结合,并运用变分贝叶斯推断方法来解决GMM模型的参数估计和模型选择问题,提出一种变分贝叶斯算法。首先,假设混合物分量个数是无限的,并根据观测数据自动确认;然后,给出变分推断的完整过程,并在此基础上提出变分贝叶斯推理算法,解决了参数估计和模型选择问题;最后,在合成数据集上进行仿真实验,实验结果表明,提出的算法收敛速度快,准确率达90%。

Gaussian Mixture Model(GMM)cannot automatically select the appropriate number of mixture components based on the observation data,which leads to the inability of GMM to accurately describe the data.In this paper,combining the Dirichlet process prior with GMM,the variational Bayesian inference method is used to solve the model parameter estimation and model selection problems.Firstly,we assume that the number of mixture components is infinite and can be automatically confirmed based on observation data.Secondly,the complete process of variational inference is given,and then,an efficient variational Bayesian inference algorithm is proposed,which can solve the problem of parameter estimation and model selection at the same time.In order to verify its validity,a lot of experiments are carried out on the synthetic data set.Experimental results show that the algorithm has a fast convergence speed and an accuracy rate of 90%.